{"id":12770,"date":"2024-03-04T15:27:35","date_gmt":"2024-03-04T09:57:35","guid":{"rendered":"https:\/\/tsboardsolutions.in\/?p=12770"},"modified":"2024-03-05T14:25:24","modified_gmt":"2024-03-05T08:55:24","slug":"ts-10th-class-maths-notes-chapter-11","status":"publish","type":"post","link":"https:\/\/tsboardsolutions.in\/ts-10th-class-maths-notes-chapter-11\/","title":{"rendered":"TS 10th Class Maths Notes Chapter 11 Trigonometry"},"content":{"rendered":"<p>We are offering <a href=\"https:\/\/tsboardsolutions.in\/ts-10th-class-maths-notes\/\">TS 10th Class Maths Notes<\/a> Chapter 11 Trigonometry to learn maths more effectively.<\/p>\n<h2>TS 10th Class Maths Notes Chapter 11 Trigonometry<\/h2>\n<p>\u2192 Trigonometry is the study of relationship between the sides and angle of a triangle.<\/p>\n<p>\u2192 Ratios of the sides of a right triangle with respect to its acute angle are called trigonometric ratios of the angle.<\/p>\n<p>\u2192 An equation involving trigonometric ratios of an angle is called a trigonometric identity. If it is true of all values of the angle.<\/p>\n<p>\u2192 Let us consider \u0394ABC in which \u2220B = 90\u00b0, A and C are acute angles. Let us study the ratios of the sides of \u0394ABC with respect to the acute angle A.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-12774\" src=\"https:\/\/tsboardsolutions.in\/wp-content\/uploads\/2023\/02\/TS-10th-Class-Maths-Notes-Chapter-11-Trigonometry-1.png\" alt=\"TS 10th Class Maths Notes Chapter 11 Trigonometry 1\" width=\"231\" height=\"199\" \/><br \/>\nsine of \u2220A = sin A = \\(\\frac{\\text { Side opposite to angle } \\mathrm{A}}{\\text { Hypotenuse }}=\\frac{\\mathrm{BC}}{\\mathrm{AC}}\\)<br \/>\ncosine of \u2220A = cos A = \\(\\frac{\\text { Side adjacent to angle } \\mathrm{A}}{\\text { Hypotenuse }}=\\frac{\\mathrm{AB}}{\\mathrm{AC}}\\)<br \/>\ntangent of \u2220A =tan A = \\(\\frac{\\text { Side opposite to angle } A}{\\text { Side adjacent to angle } A}=\\frac{B C}{A B}\\)<\/p>\n<p>\u2192 cosec A = \\(\\frac{1}{\\sin A}\\)<br \/>\nsec A = \\(\\frac{1}{\\cos A}\\)<br \/>\ncot A = \\(\\frac{1}{\\tan A}\\)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/tsboardsolutions.in\/wp-content\/uploads\/2022\/12\/TS-Board-Solutions.png\" alt=\"TS 10th Class Maths Notes Chapter 11 Trigonometry\" width=\"161\" height=\"15\" \/><\/p>\n<p>\u2192 If one of trigonometric ratios of an acute angle is known the remaining trigonometric ratios of the angle can be easily determined.<\/p>\n<p>\u2192 Trigonometric ratios of 0\u00b0, 30\u00b0, 45\u00b0, 60\u00b0 and 90\u00b0.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-12773\" src=\"https:\/\/tsboardsolutions.in\/wp-content\/uploads\/2023\/02\/TS-10th-Class-Maths-Notes-Chapter-11-Trigonometry-2.png\" alt=\"TS 10th Class Maths Notes Chapter 11 Trigonometry 2\" width=\"568\" height=\"390\" srcset=\"https:\/\/tsboardsolutions.in\/wp-content\/uploads\/2023\/02\/TS-10th-Class-Maths-Notes-Chapter-11-Trigonometry-2.png 568w, https:\/\/tsboardsolutions.in\/wp-content\/uploads\/2023\/02\/TS-10th-Class-Maths-Notes-Chapter-11-Trigonometry-2-300x206.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><br \/>\nNote : From the above table we can observe that \u2220A increases from 0\u00b0 to 90\u00b0, sin A increases from 0 to 1 and cos A decreases from 1 to 0.<\/p>\n<p>\u2192 Trigonometric ratios of complementary angles : Two angles are said to be complementary angle if their sum equals to 90\u00b0.<\/p>\n<ul>\n<li>sin (90\u00b0 &#8211; A) = cos A;<\/li>\n<li>cosec(90\u00b0 &#8211; A) = sec A<\/li>\n<li>cos (90\u00b0 &#8211; A) = sin A;<\/li>\n<li>sec(90\u00b0- A) = cosec A<\/li>\n<li>tan (90\u00b0 &#8211; A) = cot A;<\/li>\n<li>cot(90\u00b0 &#8211; A) = tan A<\/li>\n<\/ul>\n<p>\u2192 Trigonometric identities :<\/p>\n<ul>\n<li>sin<sup>2<\/sup>A + cos<sup>2<\/sup>A = 1<\/li>\n<li>sec<sup>2<\/sup>A &#8211; tan<sup>2<\/sup>A = 1 for 0\u00b0&lt; A &lt; 90\u00b0<\/li>\n<li>cosec<sup>2<\/sup>A &#8211; cot<sup>2<\/sup>A = 1 for 0\u00b0 &lt; A &lt; 90\u00b0<\/li>\n<\/ul>\n<p>Note : sin<sup>2<\/sup>\u03b8 = (sin \u03b8)<sup>2<\/sup> but sin\u03b8<sup>2<\/sup> \u2260 (sin \u03b8)<sup>2<\/sup><\/p>\n<p>Important Formula:<\/p>\n<ul>\n<li>sin(90\u00b0 &#8211; A) = cos A;<\/li>\n<li>cosec (90\u00b0 &#8211; A) = sec A<\/li>\n<li>cos(90\u00b0 &#8211; A) = sin A<\/li>\n<li>sec(90\u00b0 &#8211; A) = cosec A<\/li>\n<li>tan(90\u00b0 &#8211; A) = cot A<\/li>\n<li>cot(90\u00b0 &#8211; A) = tan A<\/li>\n<li>sin<sup>2<\/sup>A + cos<sup>2<\/sup>A = 1<\/li>\n<li>sec<sup>2<\/sup>A &#8211; tan<sup>2<\/sup>A = 1<\/li>\n<li>cosec<sup>2<\/sup>A &#8211; cot<sup>2<\/sup>A = 1<\/li>\n<\/ul>\n<p>Flow Chat:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-12772\" src=\"https:\/\/tsboardsolutions.in\/wp-content\/uploads\/2023\/02\/TS-10th-Class-Maths-Notes-Chapter-11-Trigonometry-3.png\" alt=\"TS 10th Class Maths Notes Chapter 11 Trigonometry 3\" width=\"837\" height=\"675\" srcset=\"https:\/\/tsboardsolutions.in\/wp-content\/uploads\/2023\/02\/TS-10th-Class-Maths-Notes-Chapter-11-Trigonometry-3.png 837w, https:\/\/tsboardsolutions.in\/wp-content\/uploads\/2023\/02\/TS-10th-Class-Maths-Notes-Chapter-11-Trigonometry-3-300x242.png 300w, https:\/\/tsboardsolutions.in\/wp-content\/uploads\/2023\/02\/TS-10th-Class-Maths-Notes-Chapter-11-Trigonometry-3-768x619.png 768w\" sizes=\"(max-width: 837px) 100vw, 837px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/tsboardsolutions.in\/wp-content\/uploads\/2022\/12\/TS-Board-Solutions.png\" alt=\"TS 10th Class Maths Notes Chapter 11 Trigonometry\" width=\"161\" height=\"15\" \/><\/p>\n<p>Aryabhatta (476 &#8211; 550 A.D):<\/p>\n<ul>\n<li>The first use of the idea of &#8216;sine&#8217; in the way we use it today was in the book Aryabhatiyam by Aryabhatta, in A.D. 500.<\/li>\n<li>Aryabhatta used the word &#8216;ardhajya1 for the half-chord, which was shortened to jya or jiva in due course.<\/li>\n<li>When the Aryabhatiyam was translated into Arabic, the word jiva was retained as it is. The word jiva was translated into sinus, which means curve, when the Arabic version was translated into Latin.<\/li>\n<li>Soon the word sinus, also used as sine, became common in mathematical texts throughout Europe. An English Professor of astronomy Edumund Gunter (1581\u00ac1626), first used the abbreviated notation &#8216;sin&#8217;.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>We are offering TS 10th Class Maths Notes Chapter 11 Trigonometry to learn maths more effectively. TS 10th Class Maths Notes Chapter 11 Trigonometry \u2192 Trigonometry is the study of relationship between the sides and angle of a triangle. \u2192 Ratios of the sides of a right triangle with respect to its acute angle are &#8230; <a title=\"TS 10th Class Maths Notes Chapter 11 Trigonometry\" class=\"read-more\" href=\"https:\/\/tsboardsolutions.in\/ts-10th-class-maths-notes-chapter-11\/\" aria-label=\"More on TS 10th Class Maths Notes Chapter 11 Trigonometry\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[16],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/posts\/12770"}],"collection":[{"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/comments?post=12770"}],"version-history":[{"count":3,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/posts\/12770\/revisions"}],"predecessor-version":[{"id":12776,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/posts\/12770\/revisions\/12776"}],"wp:attachment":[{"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/media?parent=12770"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/categories?post=12770"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/tags?post=12770"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}